$(20$ points$)$ Consider a dataset with six variables: X$1,$ X$2,$ X$3,$ X$4,$ X$5,$ and X$6.$ The covariance matrix of this dataset is given by:

$x1=[2\mathrm{.}5,2\mathrm{.}3,2\mathrm{.}1,0\mathrm{.}7]$

$x2=[0\mathrm{.}5,0\mathrm{.}8,1\mathrm{.}5,3\mathrm{.}6]$

$x3=[2\mathrm{.}2,3\mathrm{.}0,0\mathrm{.}3,2\mathrm{.}0]$

$x4=[1\mathrm{.}9,2\mathrm{.}2,1\mathrm{.}8,0\mathrm{.}3]$

$x5=[3\mathrm{.}1,2\mathrm{.}5,3\mathrm{.}2,1\mathrm{.}0]$

$x6=[2\mathrm{.}3,2\mathrm{.}8,0\mathrm{.}5,4\mathrm{.}0]$

Calculate the covariance matrix for $x1,x2,x3,x4,x5$ and $x6.$ Show your steps in the computation and provide the final covariance matrix.